The ideal gas law for isothermal process can be represented as ______, (P is the pressure and V is the volume of the gas at any stage).
PV = Constant.
An isothermal process is one carried out at constant temperature (T = constant). To see how pressure and volume relate, start from the ideal gas equation of state:
PV = nRT
Here n (number of moles) and R (universal gas constant) are fixed for a given quantity of gas, and in an isothermal process T is also held constant. The entire right-hand side nRT is therefore a constant, which leaves:
PV = constant
This is exactly Boyle's Law: at constant temperature, pressure is inversely proportional to volume, so if the gas is compressed to half its volume its pressure doubles. On a P–V diagram this traces a rectangular hyperbola.
Why the other expressions are wrong:
- P = constant describes an isobaric (constant-pressure) process, not a constant-temperature one.
- V = constant describes an isochoric (constant-volume) process.
- P/V = constant would mean pressure is directly proportional to volume, which is not implied by holding temperature fixed and has no standard place among the basic gas processes.
Hence the isothermal process is correctly represented by PV = Constant.
Important Questions from The Perfect Gas
The quantity of heat required to raise the temperature of unit mass of a material by one degree centigrade is called
The amount of heat required for converting one kilogram of a solid completely into liquid is called:
The heat that must be absorbed by ice of mass 500 g at – 10°C to take it to water at 20°C is (Specific heat of Ice is 2.2 kJ/kg K, Specific heat of water is 4.2 kJ/kg K and Latent heat of fusion of ice is 300 kJ/kg)
2 kg of substance receives 500 kJ and undergoes a temperature change from 100°C to 200°C. The average specific heat of substance during the process will be
The general law for the expansion or compression of gases is:
